Sometimes visualising a geometrical proof can make understanding it so much easier. Now mathematicians Elizabeth Slavkovsky and Oliver Knill, both of Harvard University, have taken a step in that direction with 3D printing. They have given form to a variety of mathematical shapes, recalling ancient Greek technology and even the shadows of the fourth dimension. They reckon that 3D printers, by making it easy to turn equations into objects, could become a powerful force in mathematics education. Jacob Aron

3D printing can also provide a window into higher dimensions. This intricate creation is the 3D "shadow" that would be cast by a hypothetical 4D shape known as a 24-cell. The 24-cell belongs to a group of shapes that are higher-dimensional versions of the Platonic solids - a group of five 3D shapes that are a mathematical curiosity, being the only ones to follow certain rules of symmetry.